Diagonal reduction algebra for $\mathfrak{osp}(1|2)$

Abstract

The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $(\mathfrak{G},\mathfrak{g})$ has previously been considered by Khoroshkin and Ogievetsky in the case of the diagonal reduction algebra for $\mathfrak{gl}(n)$. In this paper we consider the diagonal reduction algebra of the pair of Lie superalgebras $\left(\mathfrak{osp}(1|2)\times \mathfrak{osp}(1|2),\mathfrak{osp}(1|2)\right)$ as a double coset space having an associative diamond product and give a complete presentation in terms of generators and relations. We also provide a PBW basis for this reduction algebra along with Casimir-like elements and a subgroup of automorphisms.

24 pages; v4; attempted to improve readability and thoroughness

References in corpus (2)

• Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$
• Diagonal reduction algebra for $\mathfrak{osp}(1|2)$

Cited by in corpus (2)

• Diagonal reduction algebra for $\mathfrak{osp}(1|2)$
• Ghost center and representations of the diagonal reduction algebra of $\mathfrak{osp}(1|2)$